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Number of nX2 n X 2 arrays of occupancy after each element stays put or moves to some king-move neighbor, without consecutive moves in the same direction.

Column 2 of A221688.

Empirical: a(n) = 13*a(n-1) - 18*a(n-2) - 29*a(n-3) - 15*a(n-4) - 12*a(n-5) - 2*a(n-6).

Empirical g.f.: x*(3 - 4*x - 5*x^2 - 2*x^3 - 2*x^4) / (1 - 13*x + 18*x^2 + 29*x^3 + 15*x^4 + 12*x^5 + 2*x^6). - Colin Barker, Aug 10 2018

Some solutions for n=3:

Cf. A221688.

R. H. Hardin , Jan 22 2013

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R. H. Hardin, <a href="/A221687/b221687.txt">Table of n, a(n) for n = 1..23</a>

allocated for R. H. Hardin

Number of nX2 arrays of occupancy after each element stays put or moves to some king-move neighbor, without consecutive moves in the same direction

3, 35, 396, 4429, 49387, 550264, 6129659, 68277335, 760519092, 8471140593, 94356794511, 1051003927840, 11706726309807, 130396694392883, 1452438312980628, 16178148223958949, 180202131485051219

1,1

Column 2 of A221688

Empirical: a(n) = 13*a(n-1) -18*a(n-2) -29*a(n-3) -15*a(n-4) -12*a(n-5) -2*a(n-6)

Some solutions for n=3

..0..0....2..0....0..0....0..1....0..0....1..1....0..0....0..1....1..1....2..0

..2..4....1..2....3..2....3..1....3..2....2..0....6..0....2..2....2..0....0..4

..0..0....0..1....0..1....0..1....1..0....0..2....0..0....0..1....2..0....0..0

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nonn

R. H. Hardin Jan 22 2013

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